Sin75°/Cos75°+Cos75°/Sin15°=？
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Sin75°/Cos75°+Cos75°/Sin15°
= sin(45°+30°) / cos(45°+ 30 °) + 1 ...................Cos75°与 Sin15°相等
= （sin45°cos30°+ cos45°sin30°) / (cos45°cos30°- sin45°sin30°) + 1
= (√2/2 * √3/2 + √2/2 * 1/2 ) / (√2/2 * √3/2 - √2/2 * 1/2 ) + 1
= (√6/4 + √2/4 ) / (√6/4 - √2/4) + 1
= (√6 + √2 ) / (√6 - √2) + 1
= (√6 + √2 )^2 / (√6 - √2)(√6 + √2 ) + 1
= ( 6 + 2 √6√2 + 2) / ( 6 - 2 ) + 1
= (8 + 4√3) / 4 + 1
= 3 + √3
= sin(45°+30°) / cos(45°+ 30 °) + 1 ...................Cos75°与 Sin15°相等
= （sin45°cos30°+ cos45°sin30°) / (cos45°cos30°- sin45°sin30°) + 1
= (√2/2 * √3/2 + √2/2 * 1/2 ) / (√2/2 * √3/2 - √2/2 * 1/2 ) + 1
= (√6/4 + √2/4 ) / (√6/4 - √2/4) + 1
= (√6 + √2 ) / (√6 - √2) + 1
= (√6 + √2 )^2 / (√6 - √2)(√6 + √2 ) + 1
= ( 6 + 2 √6√2 + 2) / ( 6 - 2 ) + 1
= (8 + 4√3) / 4 + 1
= 3 + √3
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